Linear voltage controlled crystal oscillators

ABSTRACT

A LINEAR VOLTAGE CONTROLLED CRYSTAL OSCILLATOR HAVING AN AMPLIFIER VARIABLE VOLTAGE FEEDBACK CIRCUIT WITH INDUCTORS, CAPACITORS, AND VARACTORS PRODUCING A VARACTOR NETWORK IN SERIES WITH A CRYSTAL AND INDUCTANCE NETWORK THAT PROVIDE CIRCUIT OSCILLATION WHERE THE PHASE SHIFT THROUGH THE FEEDBACK CIRCUIT IS ZERO, OR AT A FREQUENCY WHERE THE REACTANCE OF THE INDUCTANCE-CAPACITANCE NETWORK CANCELS THE REACTANCE OF THE CRYSTAL NETWORK, WHICH VARACTOR NETWORK IS EASY TO ALIGN TO PROVIDE A LINEAR REACTANCE-VOLTAGE RELATION.

Feb. 2,1971

J. A. FUCHS LINEAR VOLTAGE CONTROLLED CRYSTAL OSCILLATORS Filed March12, 1969 2 Sheets-Sheet 1 s V VH W E m .n IAN A R u m 0 R 1 S2 v A I B rl.l

a ems ivou su-zwi v.

(PRIOR ART) MENTOR JA MES A. FUCHS FIG. 5. (PRIOR ART) ATTORNEY J- A.FUCHS I LINEAR VOLTAGE CONTROLLED CRYSTAL OSCILLATORS- Filed March 12.1969 2 Sheets-Sheet 2 FIG. 12.

INVENTOR JAMES A. rue/1s FIG. ll.

ATTORNEY United States Patent O 3,560,879 LINEAR VOLTAGE CONTROLLEDCRYSTAL OSCILLATORS James A. Fuchs, Palo Alto, Calif., assignor, bymesne assignments, to the United States of America as represented by theSecretary of the Navy Filed Mar. 12, 1969, Ser. No. 806,641 Int. Cl.H03b 5/36 US. Cl. 331-116 5 Claims ABSTRACT OF THE DISCLOSURE A linearvoltage controlled crystal oscillator having an amplifier variablevoltage feedback circuit with inductors, capacitors, and varactorsproducing a varactor network in series with a crystal and inductancenetwork that provide circuit oscillation where the phase shift throughthe feedback circuit is zero, or at a frequency where the reactance ofthe inductance-capacitance network cancels the reactance of the crystalnetwork, which varactor network is easy to align to provide a linearreactance-voltage relation.

BACKGROUND OF THE INVENTION This invention relates to linear voltagecontrolled crystal oscillators with an output that is a linearly varyingfrequency controlled by a direct current (DC) slewing voltage.

The commonly used voltage controlled crystal oscillators can beseparated into two parts, an amplifier and a DC. variable voltagefeedback network containing the crystal. This configuration is usuallyarranged so that oscillation occurs at a series resonance of thefeedback circuit. Several types of feedback networks may be used toachieve a linear frequency versus DC. voltage curve, but in the mostused prior art varactor diodes are used as voltage variable capacitorstogether with a single crystal and an appropriate embedding network.Other techniques involving multiple crystals, diode shaping networks forthe slewing voltages, or current variable inductances, areunsatisfactory from a practical standpoint because of the difficulty ofalignment, or the temperature sensitivity, or the hysteresis effects, orthe high current consumption.

SUMMARY OF THE INVENTION In the present invention several embodimentsare shown and described having novel arrangements of the varactornetwork in the feedback circuit of the oscillator amplifier that provideease of alignment and low temperature sensitivity of linearity. In thisinvention two varactor diodes and two inductances are used incombination in a varactor network along with a DO. blocking capacitor toapproximate a linear reactance-voltage relation. This varactor networkis in series with a parallel coupled crystal and inductance that areresonant at the oscillator frequency. A slewing 'D.C. voltage is appliedas an input to the varactor network to cause the frequency of theoscillator output to change a slight amount. The inductance in thecrystal-inductor parallel network is chosen to exactly cancel orneutralize the crystals shunt capacity. The crystal can then beconsidered a series inductor-capacitor network in the small range offrequencies of interest, and in this range the reactance-frequencyfunction of the neutralized crystal will be very linear. It is thereforea general object of this invention to provide a voltage controlledcrystal oscillator circuit with a highly linear voltage relation to thereactance that is easy to align and with low temperature sensitivityaffecting linearity.

BRIEF DESCRIPTION OF THE DRAWING These and other objects and theattendant advantages,

3,560,879 Patented Feb. 2, 1971 features, and uses will become moreapparent to those skilled in the art as a more detailed descriptionproceeds when taken in view of the accompanying drawing, in which:

FIG. 1 shows in partial circuit schematic and partial block diagram of avoltage controlled crystal oscillator known in the prior art;

FIGS. 2, 3, and 4 illustrate reactance curves for the circuit of FIG. 1;

FIGS. 5 and 6 illustrate prior art voltage controlled crystal oscillatorcircuits;

FIGS. 7, 8, 9, and 10 are partially schematic and partially blockdiagrams of four embodiments of linear voltage controlled crystaloscillators in accordance with this invention;

FIG. 11 is a circuit schematic diagram of a linear voltage controlledcrystal oscillator coupled to an amplifier circuit in accordance withthis invention; and

FIG. 12 is a reactance-voltage curve illustrating the results obtainablein the circuits of FIGS. 7 through 10.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIGS. 1, 2, and 3,there is illustrated a voltage controlled crystal oscillator of oneknown type consisting primarily of an amplifier 10 and a feedbackcircuit which includes a crystal network C 1 and a varactor network D LA DC. voltage is applied to the feedback circuit from a terminal 11through a resistor 13 to slew the oscillator frequency, and a biasvoltage is applied to the feedback at terminal 12. The crystal C and itspole-zero condition are illustrated in FIG. 2 where the reactance,positive and negative, are illustrated with respect to the frequency inradians where w=21rf. The varactor diode D has a capacitance-voltagerelation of D =k./V where k is a constant and /ssotg /z. The reactanceversus voltage of the series D L network in FIG. 1 is:

and FIG. 3 illustrates the reactance-voltage curve. The circuit of FIG.1 oscillates at the frequency where the phase shift through the feedbackcircuit is zero; that is, at the frequency where the reactance of thevaractor network D L cancels the reactance of the crystal network C,,L,,. Both the reactance-voltage function of the D L network and thereactance-frequency curce of the C,, L network are highly nonlinear, buta properly selected inductor, L placed across the crystal, C can yield aa feedback circuit whose zero reactance point, and therefore theoscillation frequency, versus voltage is highly linear. When L iscorrectly chosen, the reactance of the C,, L network will have a fastrate of change as a function of frequency at those negative reactanceswhere the D L network has a slow rate of change as a function ofvoltage, and vice versa. Thus a linear oscillation frequency versusvoltage function is nearly obtained.

Referring more particularly to FIGS. 4, 5, and 6 a second type of priorart voltage controlled oscillators is diagrammed in FIGS. 5 and 6. Inthese two figures the inductor, L,,, is chosen to exactly cancel orneutralize the reactance of the crystals, C shunt capacity. The crystalnetwork can then be considered to be a series L-C circuit in the smallrange of frequencies of interest, and in this range thereactance-frequency function of the neutralized crystal will be verylinear. This may be shown by the following equations:

3 Let, w=21rf l X (L0 The slope of the reactance is:

dx 1 F.

The deviation of the slope from a straight line (constant slope) can bedetermined from the second derivative:

QL -92! dw 0: 0 Aw 2 Aw JC}? Now at series resonance 2 an Therefore,

2 M 2L and,

& at vM e f 0 Thus, if the slewing voltage is varied to slew theoscillator frequency 1%, the slope of the crystals reactance-frequencycurve will change only 1% over this frequency range.

Maintaining the crystal network linear, efforts are directed towarddeveloping a varactor network whose reactance versus voltage curve islinear. The prior art circuits of FIGS. and 6 approximate this linearcondition. The capacitor, Q, in the varactor network, L L (L D (D C isselected to have a very small reactance at the oscillator frequency.Considering the varactor networks alone, the following reactanceequation is used:

AV-w B V" .0 0

where A, B, C depend on the circuit configuration and the desiredsensitivity of the overall circuit. FIG. 4 is a reactance-voltage plotfor a fixed frequency, but in the actual oscillator Where frequencychanges only l%2% and reactance may change a large factor, the plot isstill valid. Proper choice of circuit components will make the actualreactance curve tangent to the desired curve at the mid range where thedashed line meets the curved line in FIG. 4.

The voltage controlled crystal oscillator of FIG. 1 using the meansabove to improve linearity can be constructed but has severaldisadvantages. This circuit is difficult and time consuming to alignsince the 0,, L reactance must be adjusted very precisely to complementthe varactor curve. This adjustment is dilficult since the proximity ofthe seriesand parallel resonances of the crystal make for a verysensitive network. This reactance sensitivity also makes the circuitsslewing linearity highly temperature sensitive.

The circuits of FIGS. 5 and 6 avoid some of the difficulties of FIG. 1but are easy to align, the value of L is not critical, and thetemperature sensitivity of the linearity is low. However, these circuitshave two deficiencies; the designer has no control over linearity andimpractically large inductor values may often result. Since the desiredstraight line is being approximated essentially by a second order curve,the actual linearity may deviate substantially from the straight line.

'In the present invention, as illustrated in the several embodiments byFIGS. 7 through 12, the advantages of ease of alignment and lowtemperature sensitivity of li e i y, as described above for FIGS. 5 and6, are re- 4 tained and the designer has full control over the linearityof the circuit. FIGS. 7 through 10 illustrate four diiferent embodimentsin the feedback circuits which may be used in a linear voltagecontrolled crystal oscillator.

FIG. 7 shows the varactor network of the feedback circuit with theinputbeing the amplifier 10 output coupled in common to the anodes of Dand D one terminal of L and one terminal of resistor 13 through which isapplied the slewing voltage 11. The output of the varactor network istaken from the cathode of D which is connected in common with a terminalof inductor L and resistor 14 through which is connected bias voltage12. The remaining terminal of inductor L is connected in common with aterminal of coupling capacitor C and the cathode of D The remainingterminal of C is connected to the remaining terminal of L FIG. 8, withlike parts in FIG. 7 having the same reference characters, differs fromFIG. 7 in that the amplifier 10 output, being the varactor networkinput, is the common connection of the anode of D and one terminal of Land C FIG. 9, shows the embodiment with an inductor L in parallel withthe varactor diode D and an inductor L in parallel with the varactordiode D the DC. blocking capacitor C being in the coupling between thecommonly coupled varactor diode cathodes and the commonly coupledterminals of the inductors L and L FIG. 10 is similar to FIG. 8 exceptthat the output of the varactor network is taken from the commonvaractor diode cathode connection at the voltage biasing point. In allthe FIGS. 7 through 10 the blocking capacitor C has a very low reactanceat the oscillator frequency.

Referring more particularly to FIG. 11 there is illustrated a circuitschematic of the amplifier 10 and the varactor and crystal networks inthe feedback circuit. The crystal C, is completely neutralized, or whenthe reactance of the inductor L exactly cancels the reactance of thecrystal C and it behaves as a series circuit. In the varactor networkthe varactor diodes D and D are oriented as in FIG. 8 with the inductorL and the capacitor C in the same relative position. An adjustableinductor L and a fixed inductor L in series are coupled across thevaractor diodes. The slewing voltage applied to terminal 11 is connectedto the common cathode coupling of the varactor diodes, as in FIG. 7. Inthis FIG. 11, L may be 8-12 microhenrys (,uh), L =15 [.Lh, C =.0lmicrofarads t), resistor l3=51K ohms, and the varactor diode D may betype IN1542, and varactor diodes D may be type IN1544 for one operativeexample of feedback for the amplifier 10.

The reactance expression for the varactor networks in FIGS. 7 through 10is:

The constants R, S, T, and U depend on the particular circuit, thesensitivity, the linearity, and the frequency. FIG. 12 is a reactanceversus voltage diagram with a straight dashed line showing the desiredlinear function of the feedback circuit for the oscillator. The curvedline overlying the dashed line is essentially approximated by a cubicfunction. The four feedback circuits (FIGS. 7-10) may approximate astraight line to an arbitrary accuracy but it remains to determine theconstants R, S, T, U for a specified linearity and sensitivity and tosynthesize the desired networks. To find the four constants, a system offour equations must be solved. Two equations are obtained by forcing thereactance equation to fit the desired reactance equation at the endpoint voltages, V and V, as seen in FIG. 12. Using the equations derivedabove for neutralized crystal sensitivity, the following equations aredeveloped:

where;

L =crystal series inductance in henrys S=oscillator slewing sensitivityin hertz per volt.

l=desired decimal linearity.

The factor 1/2 is included as a safety factor. The factor (ll/2) forcesthe reactance at V and V to deviate from the desired straight line by afactor of U2. The system of four equations may now be expressed as:

W am swell] where;

i=1 to 4 w =radian oscillator frequency at center of voltage range,

u=diode junction factor These equations may be solved for R, S, T, Uwhen w and a are given which solution is feasible on a digital computer.With the solution of R, S, T, & U the varactor networks can besynthesized. In the complex plane the reactance equation above has theimpedance function:

The impedance function Z(p) is synthesized in the standard Foster andCaner forms to obtain the networks shown in the FIGS. 7 through 10.Other forms are possible at the expense of additional components. Theparts values resulting from the synthesis are the following: Feedbackcircuit in FIG. 7:

Feedback circuit in FIG. 8:

D C(B-A) Feedback circuit in FIG. 10:

Solution of the above equations have not been made herein since thesesolutions are of the nature to be completed by a computer. Thecomputations are made as set forth in the text Network Analysis AndSynthesis by Louis Weinberg, published by the McGraw-Hill Book Company,Inc., 1962, Chapter 9, where there is a complete discussion of theFoster and Cauer synthesis methods. The solution of the four equationsrelated respectively to the varactor feedback circuits of FIGS. 7through 10 will provide a linear function of the reactance relative tothe slewing DC. voltage applied.

While modifications and changes may be made in the constructionaldetails and features of this invention and remain within the spirit ofmy invention, I desire to be limited in my invention only by the scopeof the appended claims.

I claim:

1. A linear voltage controlled crystal oscillator circuit comprising:

an amplifier having an input and an output; and

a feedback circuit including a varactor network and a crystal networkcoupled in series from the output to the input of said amplifier, saidvaractor network having a pair of varactor diodes in series, a pair ofinductors paralleling said varactor diodes, and a blocking capacitorbetween said amplifier output and the juncture of said varactor diodeswith variable slewing voltage and biasing voltage inputs coupled to saidvaractor network to provide a linear reactance with respect to saidapplied variable slewing voltage, and said crystal network having acrystal in parallel with an inductance with the inductive reactancethereof exactly canceling the capacitive reactance of said crystal tooperate as a series inductance-capacitance network whereby the reactanceof said feedback circuit is substantially linear in a predeterminedfrequency range.

2. A linear voltage controlled crystal oscillator circuit as set forthin claim 1 wherein said pair of varactor diodes have the anodes thereofcoupled in common to said amplifier output and to said slewing voltageinput, one of said pair of inductors and said blocking capacitor inseries being coupled in parallel to one of said varactor diodes, theother of said pair of inductors being in parallel to said pair ofvaractor diodes, and the cathode of said other of said pair of varactordiodes being coupled to said biasing voltage and to said crystalnetwork.

3. A linear voltage controlled crystal oscillator circuit as set forthin claim 1 wherein said pair of varactor diodes are incathode-to-cathode coupled relation to said biasing source with oneinductor and said blocking capacitor in series coupled in parallel withone of said varactor diodes and with the other inductor coupled inparallel to the series coupled varactor diodes, the slewing voltage andthe amplifier output being coupled to the anode of said one varactordiode and the anode of the other varactor diode being coupled to saidcrystal network.

4. A linear voltage controlled crystal oscillator circuit as set forthin claim 1 wherein said pair of varactor diodes have their cathodescoupled in common to said bias voltage, said pair of inductors in seriescoupled in parallel to the anodes of said varactor diodes with thecommon coupling of said inductors and the common coupling of saidvaractor diodes coupled to opposite plates of said blocking capacitor,and said slewing voltage coupled with said amplifier output to the anodeof one of said varactor diodes, and the anode of said other ReferencesCited varactor diode being coupled to said crystal network. UNITEDSTATES P T 5.A1 lt tlld t1 llt 't gij fgg fi ggfi fig 6 a 9 mm 3,358,24412/1967 Ho et a1. 331 177 v x said pair of varactor diodes have theircathodes coupled 5 3477039 11/1969 Chan 331 116 in common to saidbiasing source and to said crystal network, the anode of one coupled tosaid ampli- JOHN KOMINSKI Pnmaly Exammer fier output and said slewingvoltage, the anode of S- H- GRIMM, Assistant EXamirler the other coupledthrough one of said pair of inductors to said amplifier output and saidslewing 10 voltage, and the other of said pair of inductors in331-158,177 series With said blocking capacitor coupled in paralto saidone varactor diode.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION UNDER RULE 322Patent No, 315601879 D d 2 February 197].

Inventor(s) JAMES A. FUCHS It is certified that error appears in theabove-identified patent and that said Letters Patent are herebycorrected as shown below:

Column 3, line 19, change equation To read:

Signed and sealed this 3rd day of August 1971.

(SEAL) Attest:

EDWARD M.FLE'I'GHER,JR. WILLIAM E. SCHUYLER JR Atteatin'g OfficerCommissioner of Patents

